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Livingston County Schools
Eighth Math Unit 4
Translations
Unit Overview
Students use ideas about distance and angles, how they behave under translation, rotations, reflections, and dilations, and ideas about
congruence and similarity to describe and analyze 2D figures and to solve problems.
Length of unit: days
KY Core Academic
Standard
8.G.1abc Verify
experimentally the
properties of rotations,
reflections, and
translations:
a. Lines are taken to
lines, and line segments
to line segments of the
same length.
b. Angles are taken to
angles of the same
measure.
c. Parallel lines are taken
to parallel lines.
Learning Target
K
71. I can define & identify
rotations, reflections, and
translations.
X
72. I can identify corresponding
sides & corresponding angles.
X
73. I can understand prime
notation to describe an image
after a translation, reflection, or
rotation.
X
74. I can identify center of
rotation.
X
75. I can identify direction and
degree of rotation.
X
76. I can identify line of
reflection.
X
Reasoning Targets
77. I can use physical models,
transparencies, or geometry
software to verify the properties
of rotations, reflections, and
translations (ie. Lines are taken
to lines and line segments to line
segments of the same length,
angles are taken to angles of the
R
X
S
P
Critical Vocabulary
Texts/Resources/Activities
rotations,
reflection rigid
transformation,
translations,
image,
Crosswalk Lesson 24
Lesson 7-7 p. 358
Transformations
8.G.2 Understand that a
two-dimensional figure
is congruent to another
if the second can be
obtained from the first
by a sequence of
rotations, reflections,
and translations; given
two congruent figures,
describe a sequence that
exhibits the congruence
between them.
same measure, & parallel lines
are taken to parallel lines.)
78. I can define congruency.
79. I can identify symbols for
congruency.
X
Reasoning Targets
80. I can apply the concept of
congruency to write congruent
statements.
Reasoning Targets
85. I can describe the effects of
dilations, translations,
rotations, & reflections on 2-D
figures using coordinates
86. I can define similar figures
as corresponding angles are
rotations,
reflection,
translations,
image, rigid
transformation
Crosswalk Lesson 24
Lesson 7-6 p. 354
Congruence
Translation,
rotation, dilation,
enlargement,
image, reduction,
rigid
transformation,
scale factor
Crosswalk Lesson 24-25
Lesson 5-6 p. 244
Dilations
AA Angle-angle
similarity, SAS side
Crosswalk Lesson 25-26
Lesson 5-5 p. 238
X
81. I can reason that a 2-D
figure is congruent to another
if the second can be obtained
by a sequence of rotations,
reflections, translation.
82. I can describe the
sequence of rotations,
reflections, translations that
exhibits the congruence
between 2-D figures using
words.
8.G.3 Describe the effect 83. I can define dilations as a
of dilations, translations, reduction or enlargement of a
rotations, and
figure.
reflections on twodimensional figures
84. I can identify scale factor of
using coordinates.
the dilation.
8.G.4 Understand that a
two-dimensional figure
X
X
X
X
X
X
X
is similar to another if
the second can be
obtained from the first
by a sequence of
rotations, reflections,
translations, and
dilations; given two
similar two-dimensional
figures, describe a
sequence that exhibits
the similarity between
them.
8.G.5 Use informal
arguments to establish
facts about the angle
sum and exterior angle
of triangles, about the
angles created when
parallel lines are cut by a
transversal, and the
angle-angle criterion for
similarity of triangles.
For example, arrange
three copies of the same
triangle so that the
three angles appear to
form a line, and give an
congruent and corresponding
sides are proportional.
87. I can recognize symbol for
similar.
X
Reasoning Targets
88. I can apply the concept of
similarity to write similarity
statements.
Similar Triangles
Angle-angle
similarity, alternate
interior, alternate
exterior,
corresponding
angles, exterior
angles, interior
angle, similar
triangles, straight
angle,
supplementary,
transversal,
Crosswalk Lesson 26-28
Lesson 7-2 p. 330
Parallel and Perpendicular
Lines
X
89. I can reason that a 2-D
figure is similar to another if the
second can be obtained by a
sequence of rotations,
reflections, translation, or
dilation.
X
90. I can describe the sequence
of rotations, reflections,
translations, or dilations that
exhibits the similarity between
2-D figures using words and/or
symbols.
91. I can define similar
triangles.
X
X
92. I can define and identify
transversals.
X
93. identify angles created
when parallel line is cut by
transversal. (alternate interior,
alternate exterior,
corresponding, vertical,
adjacent, etc.)
X
Reasoning Targets
94. I can justify that the sum of
angle side
similarity, dilation,
enlargement,
reduction, scale
factor, similar
triangles
X
argument in terms of
transversals why this is
so.
interior angles equals 180. (For
example, arrange three copies
of the same triangle so that the
three angles appear to form a
line.)
95. I can justify that the
exterior angle of a triangle is
equal to the sum of the two
remote interior angles.
96. I can use Angle-Angle
Criterion to prove similarity
among triangles. (Give an
argument in terms of
transversals why this is so.)
Common Assessments Developed (Proposed Assessment
Dates):
X
X
HOT Questions: